During the last two decades, quantum information has proven, both theoretically [1]} and experimentally [2]}, to have made several advances and to provide the key tools for a modern technological revolution. These advances are mainly due to the prospects of quantum communications [3]}, [4]}, [5]} and quantum computers [6]}, [7]}, [8]}, [9]} that allow to storage, process and transform information using quantum mechanical systems. Besides, several quantities of interest in quantum information theory are not completely accessible via observation and cannot be directly evaluated by quantum measurements [10]}, [11]}, [12]}. One may quote for instance ; a quantum phase [13]}, the purity of a quantum state [14]} or quantum correlations [15]}. In all these cases, one must resort to indirect measurement and deduce the value of the quantity of interest from its inuence on a given source. The canonical way to deal with this problem is to use the tools of quantum estimation theory [16]}, [17]}. For example, during the famouse LIGO experiment [18]}, the gravitational wave inserted a relative phase into the light source which is not a directly measurable quantity, however this phase was estimated through the interference pattern observed.
